Position measuring transformer

ABSTRACT

Disclosed is a position-measuring transducer which is more uniformly accurate from one position to another in the presence of undesired anomalies. The transducer has at least one winding formed from two continuous, printed winding sections where those sections are spacially arrayed and electrically connected to neutralize error-causing couplings. A two-phase embodiment includes sine and cosine windings each arrayed in two layers, all of which are combined together opposite each other in a fourlayer structure. Additional embodiments include a two-layer linear transducer, a four-layer multi-cycle rotary transducer, and a four-layer single-cycle rotary transducer. In those embodiments, the sine and cosine windings individually are structured to neutralize unwanted coupling and provide compensation for quadrature error within each space cycle. Quadrature compensation and harmonic cancellation techniques are employed. Two continuous winding sections per winding achieve smooth, uniformly low errors with reduced sensitivity to undesired anomalies.

United States Patent [1 1 Farrand et a1.

[451 Nov. 13, 1973 [21] Appl. No.: 234,792

[52] US. Cl 323/46, 336/10, 336/123, 336/129, 336/200 [51] Int. Cl. 1101121/04 [58] Field of Search 336/115, 122, 123, 336/129, 200, 5, 10, 12; 323/46, 53

[56] References Cited UNITED STATES PATENTS 3,466,580 9/1969 Bull 336/200 X 2,685,070 7/1954 Childs 336/123 3,673,584 6/1972 Farrand 336/129 X 3,668,587 6/1972 Foster 336/123 2,867,783 1/1959 Childs 336/123 2,915,721 12/1959 Farrand et al. 336/123 X 3,587,019 6/1971 Bull 336/200 3,441,888 4/1969 Farrand 336/123 3,148,347 9/1964 Morrison 336/123 Primary Examiner-Thomas J. Kozma Attorney-William E. Beatty et al.

[5 7] ABSTRACT Disclosed is a position-measuring transducer which is more uniformly accurate from one position to another in the presence of undesired anomalies. The transducer has at least one winding formed from two continuous, printed winding sections where those sections are spacially arrayed and electrically connected to neutralize error-causing couplings. A two-phase embodiment includes sine and cosine windings each arrayed in two layers, all of which are combined together opposite each other in a four-layer structure.

Additional embodiments include a two-layer linear transducer, a four-layer multi-cycle rotary transducer, and a four-layer single-cycle rotary transducer. in those embodiments, the sine and cosine windings individually are structured to neutralize unwanted coupling and provide compensation for quadrature error within each space cycle. Quadrature compensation and harmonic cancellation techniques are employed. Two continuous winding sections per winding achieve smooth, uniformly low errors with reduced sensitivity to undesired anomalies.

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COS(I,'II) A 0 POSITION MEASURING TRANSFORMER BACKGROUND OF THE INVENTION This invention relates to position-measuringtransducers and particularly to position-measuring transformers which include two relatively movable members. One member typically carries two planar windings (called polyphase windings) whichare phase shifted in space relative to each other and which are inductively coupled to another planar winding (called the single phase winding) carried by the other member. Either or both members may have single or polyphase windings.

In practice, position-measuring transformers have included on the single-phase member, a single winding formed from uniformly spaced, series-connected active conductors where adjacent conductors conduct in opposite directions. In practice, for linear devices the single phase member is called the scale and for rotary devices it is called the rotor.

The other relatively movable member, called the polyphase member, of position-measuring transformers generally includes two polyphase windings, each phaseshifted in space with respect to the other thereby presenting two different space phases to the other member.

Conventionally, the poly-phase member is called the slider" in the case of linear devices and the stator in the case of rotary devices.

The phase-shift between the polyphase windings may be one quarter of the space cycle of the single phase winding. When the polyphase windings are shifted a quarter cycle, they are conventionally identified as the sine and cosine windings. While sine and cosine windings are conventional, other phase shifts such as 120 may be implemented.

When one winding on one member of a positionmeasuring transformer is energized with an alternating primary signal, a coupling signal, sometimes called a coupling wave, is induced in any winding on the other member of the position-measuring transformer to which it is in close proximity. For accurate measurements, it is desired to have the coupling between windings vary precisely as an unbiased sinusoid as a function of the relative space displacement of the windings over each space cycle. The space cycle is equal to twice the spacing, P, between conductors, that is, the space cycle equals 2?. The space frequency,or more precisely, the fundamental space frequency, is defined as the reciprocal, l/(ZP), of the space cycle. For an ideal system, the coupling between windings is a perfect sinusoid which has a fundamental space frequency 1/(2P).

It is well known in the prior art that positionmeasuring transformers tend to have a' coupling which is not precisely sinusoidal or is not zero biased. Usually, the coupling includes coupling components resulting from the higher order harmonics of the fundamental space frequency, particularly, the higher order odd harmonics. Also, unwanted coupling components result from coupling at less than the fundamental frequency, particularly from a constant coupling (zero frequency coupling). Constant coupling is the coupling which results from a constant field which does not'vary as a function of space position (hence zero frequency) or from a variable field with a constant bias term (zero frequency term). Constant coupling is sometimes referred to as one turn loop coupling. Coupling other than at the fundamental space frequency between the windings of a position-measuring transfonner gives rise to unwanted errors in position measurement, and, therefore, is to be avoided.

U.S. Pat. No. 2,650,352 to Childs discloses a transducer having a continuous winding on one member inductively coupled to a continuous winding on the other member. In transducers of that type, the accuracy of position measurement is limited because the coupling between the two windings as a function of their relative space positions is not precisely sinusoidal. The lack of sinusoidal coupling is due in part because of the inductive constant coupling component (zero frequency component) which occurs between the windings. Such inductive constant coupling gives rise to an error term which is identified as a once per cycle or as a fundamental error term.

In U.S. Pat. No. 2,799,835 to R. W. Tripp, et al., a number of techniques are disclosed for obtaining a more precisely sinusoidal coupling between members of a position-measuring transformer. In order to avoid constant coupling, one or more of the windings is divided into a plurality of winding sections where one- 'half the sections for any winding are connected in a positive fashion with respect to the constant coupling and the other half are connected in a negative fashion with respect tothe constant coupling. When the positive and negative sections are electrically connected together, the constant coupling components tend to cancel.

U.S. Pat. No. 2,799,835 also discloses additional techniques for rendering the windings of positionmeasuring transformers more nearly sinusoidal, particularly with respect to unwanted coupling at higher order harmonics of the fundamental frequency. Conductor-to-space width ratios, inclination of the active conductors and the spacing of electrically connected groups of winding sections are examples of techniques used.

U.S. Pat. No. 2,915,721 to C.L. Farrand discloses a transducer wherein one-half-current return conductors are employed to establish field patterns which tend to minimize the constant coupling between the members of a position-measuring transformer. The one-halfcurrent return conductors are arrayed parallel to the end conductors on the single phase winding of a position-measuring transformer.

In U.S. Pat. No. 2,915,722 to V. F. Foster, the constant coupling neutralization is achieved by having onehalf the winding sections for each of the polyphase windings (sine and cosine) connected in opposition to the other half with respect to the constant coupling.

In addition to the object of having precisely sinusoidal coupling between windings, two-phase systems also desirably have two windings which are precisely in quadrature, that is, are spaced apart precisely onequarter of the space cycle. Lack of quadrature between polyphase windings results in measurement errors which are identified as out-of-phase second harmonic errors.

In order to insure more exact quadrature between windings, the above referenced U.S. Pat. No. 2,915,722 employs a form of quadrature compensation. The lack of exact quadrature in that patent results from variations in length like those caused by temperature change. Similarly, U.S. Pat. No. 3,441,888 to C. L. Farrand employs a form of quadrature compensation in a transducer having a large plurality of sine and cosine winding sections arrayed opposite each other.

While all of the above-described techniques have contributed to position-measuring transformers capable of accurate measurements, still further improvements in accuracy and in manufacturing techniques are desirable.

One problem with prior art transducers is their sensitivity to error-causing anomalies which produce a lack of smoothness which is characterized by irregularities in the accuracy of measurement from one space position to another. Anomalies result, for example, at the junction between the end-to-end abutted bar scales which form the continuous reference winding of a transformer. The junctions between end-to-end abutting bar scales tend to produce anomalies in the coupling field. Other types of anomalies result, for example, from defects or irregularities in materials, from deformity of conductor patterns, from non-uniformity of the air gap such as occurs, for example, with a buckle in a tape scale, and from terminal pins and leads.

In order to avoid errors in the prior art, the unwanted coupling of one winding section in one space area is compensated for by the unwanted coupling of another winding section in a different space area. The degreeof compensation and therefore the degree of error reduction is dependent upon a non-varying coupling relationship for the two different areas. A number of factors, however, cause variances in the coupling of different areas and therefore produce deleterious effects in the operation of transducers relying on the compensation of one different area against another. For example, an anomaly which only couples to one of the two space areas at a time disturbs the compensating relationship.

Prior art transducers capable of accurate measurements have been generally of the non-continuous type, that is, having windings formed from a large number of winding sections. Non-continuous windings are a problem, however, because the field patterns for the first and last active conductors for each winding section are unopposed and are therefore irregular compared to the precise alternating patterns of the internal active conductors. These irregularities attendant the first and last conductors of each winding section produce measurement errors particularly when they couple with other anomalies such as the junction between two scales of a reference winding. Because of these errors,- the greater the number of winding sections, the greater the number of errors due to first and last conductor end effect irregularity.

In addition to the end effects problem, prior art transducers have employed sine and cosine winding sections separated by larger displacements than the desired minimum of one-quarter of the space cycle. When those sine and cosine winding sections translate across an anomaly, the sine winding section is disturbed at a different time than the cosine winding section and, therefore, an error occurs due to the unwanted change in ratio of the sine and cosine coupling.

In light of the above background of the invention, it is an object to provide transducers which in various combinations have reduced sensitivity to anomalies, have more uniform accuracy, have quadrature (or other phase) compensation, have constant coupling reduction, and have cancellation of undesired harmonics.

SUMMARY OF THE INVENTION The present invention is a position-measuring transformer including relatively movable members where each member has one or more windings reactively coupled to one or more windings on the other member. The windings are structured so as to tend to make the coupling between windings precisely a sinusoid which varies as a function of the relative space position of the movable members.

Referring to Background of the Invention" above, the statement is made that further improvement in accuracy and manufacturing techniques are desirable. Such improvements and techniques beyond the mentioned prior art as made by this invention are described in detail later and include: equality of gain between quadrature compensating windings; quadrature compensation within one cycle; end conductors shifted to conduct in opposing directions to cancel error causing coupling waves; a manufacturing procedure to insure equality. of conductor or sector spacing errors; averaging of conductor widths to maintain a specific width-tospace ratio; and cancellation of miscellaneous unwanted end effect fields.

In one embodiment of thepresent invention, un-

' wanted constant coupling.

In a two-phase embodiment of the present invention, sine and cosine quadrature windings are each arrayed in different layers in superposed relation to form a multi-layer structure. In one arrangement, both the sine and cosine windings consist of only two winding sections each. Those winding sections are continuous printed conductors arrayed opposite each other on different layers where the two winding sections for each layer are electrically additive with respect to the fundamental signal while tending to neutralize the unwanted constant coupling.

In a further multilayer embodiment, the four winding sections which form the sine and cosine windings are arrayed so as to employ quadrature compensation. Specifically, through manufacturing techniques the relative space position of one sine winding section to one cosine winding section is maintained substantially identical to the relative space position of the other sine winding section to the other cosine winding section. As a result of that identity and even though the sine and cosine winding sections are not exactly in quadrature, the resultant coupling tends to be exactly in quadrature. In one embodiment, the four winding sections are each in a different layer and are arrayed opposite each other to form a four-layer structure. Each of the winding sections in that four-layer structure, extends over the approximate same length and couples, therefore, to the same space area. In another embodiment, the four manner whereby the ratio of the sine and cosine coupling to the other member tends to be unchanged by the anomaly. In one embodiment, the sine and cosine windings are arranged with winding sections on four layers in superposed relation wherein the space separation of the active conductors of the winding sections does not substantially vary from 90 degrees.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 depicts in accordance with the present invention a schematic representation of a single winding (shown solid), for location on one member, in inductive coupling relationship to another winding for location on another member, wherein the latter winding is formed from a first winding section (shown dotted) on one layer arrayed opposite a second winding section (shown broken) on another layer.

FIG. 2 depicts a representation of the alternating field pattern conductors is equal to the generated by the FIG. 1 transformer.

FIG. 3 depicts waveforms representative of the FIG. I apparatus coupling signals.

FIG. 4 schematically depicts two arrays of approximately 90-shifted active conductors formed on one sheet in prior relation to provide, after further steps, two layers of conductors fora multilayer transformer member in accordance with the present invention.

FIG. 5 schematically depicts a second pattern identical to the pattern of FIG. 4, but shifted from left to right on the sheet to aid in the understanding of FIG. 6.

' FIG. 6 schematically depicts an overlayed combina tion of the FIG. 4 and FIG. 5 patterns including the addition of end conductors to form four separate winding sections on two layers.

FIG. 7 schematically depicts the windings for a transformer member where the windings are arrayed in a four layer structure constructed from the FIG. 4, FIG. 5, and FIG. 6 patterns.

FIG. 8 depicts a vector diagram descriptive of the quadrature compensation feature existing in the FIG. 7 windings.

FIG. 9 depicts another vector diagram for explaining the quadrature compensation feature of the FIG. 7 windings.

FIG. 10 depicts a top view of the four layers which are combined in superposed relation to form the structure schematically represented in FIG. 7.

FIG. 11 depicts a top view of overlayed terminal connections suitable for use with the winding sections of FIG. 10.

FIG. 12 depicts a representation of an enlarged cross sectional view of the active cnductors of a reference winding over four pairs of active conductors, one pair each from the four winding sections of FIG. 10, where the four pairs are arrayed in the four-layer structure represented by FIG. 7.

FIG. 13 depicts a perspective top, front view of a bro- I ken away transducer member including four layers of winding sections of the FIG. 10 type.

FIG. 14 depicts a perspective end, front view showing the multi-layer structure of the FIG. 13 winding member in its position opposite a second winding member.

FIG. 15 depicts a schematic representation of a pattern on one layer having two arrays of radial active conductors useful for constructing a multi-poled rotary transducer.

FIG. 16 is a second schematic pattern for rotary transducers substantially identical to the FIG. 15 pattern.

FIG. 17 depicts a schematic representation of the overlayed FIG. 15 and FIG. 16 patterns.

FIG. 18 is a simplified representation of the overlayed patterns derived by folding the two radial arrays of the FIG. 17 pattern opposite each other along the line 41 as shown in FIG. 20.

FIG. 19 schematically depicts four layers of winding sections formed by adding end conductor portions to the arrays of FIG. 17 and separating those arrays, for viewing clarity, in the same order as in FIG. 10.

FIG. 20 depicts a schematic representation of the four winding sections of FIG. 19 arrayed .opposite each other about a common center to form a four-layer rotary position transfonner structure.

FIG. 21 depicts a vector representation of the quadrature compensation feature which exists in the FIG. 20 device.

FIG. 22 depicts a schematic representation of a reference winding below a two-layer winding section member in which two patterns like those of FIG. 6 are placed side by side.

FIG. 23 depicts an error curve for a transducer of the present invention of the type represented by FIG. 7 and an error curve for a typical prior art transducer shown above the transducer measurement arrangement.

FIG. 24 depicts a schematic representation of a winding pattern employed as one layer in a multi-layer rotary transducer in accordance with the present invention having one cycle per revolution.

FIG. 25 schematically depicts a pattern of the FIG. 24 type rotated FIG. 26 schematically depicts a fixture and two double layer laminates useful in producing a four-layer transducer in accordance with the present invention having windings of the FIG. 24 and FIG. 25 type.

FIG. 27 depicts the fixture of FIG. 26 with the laminates arrayed for the second stage of the manufacturing process which produces quadrature compensation of the present invention.

FIG. 28 schematically depicts the four-layer configuration which results after the processing steps of FIG. 26 and FIG. 27.

FIG. 29 schematically depicts the manner in which the multi-layer structure of FIG. 28 is combined to fonn a four-layer structure.

DETAILED DESCRIPTION The transducers of the present invention are position-measuring transformers of the type frequently marketed under the registered trademark Inductosyn.

FIG. 1 depicts a representation of a position-marking transformer of the present invention in which a first winding 2 is positioned to magnetically couple to a second winding 6, the windings 2 and 6 each being on relatively movable members (not shown). The second winding 6 includes a first winding section 8 (shown in broken line) and a second winding section 9 (shown in dotted line). The first and second winding sections 8 and 9 are each typically printed copper conductors in a different layer where the layers are on opposite sides of an insulating layer to form a laminate. The actual details of typical layer thicknesses and materials are described hereinafter in connection with FIG. 13 and 14.

The first winding 2 is formed with active conductor portions having a prefix 3- and identified as 3-1, 3-2, 3-8. The active conductor portions 3- are connected in series by end conductor portions having the prefix 4- and identified in FIG. 1 as 4-1, 4-2, 4-7. The end conductors 4- are arrayed alternately along the margins defined by opposite ends of the active conductor portions 3- so that adjacent active conductor portions 3-1 conduct in opposite directions. Adjacent active conductor portions, therefore, define opposite poles and the distance between the adjacent conductor portions on either side of a given active conductor portion equals a full space cycle.

In a manner like that for fist winding 2, each of the winding sections 8 and 9 for the second winding 6 is also formed of active conductor portions connected by end conductor portions along alternate margins.

Specifically, winding section 8 has active conductor portions having prefixes 18- and identified as 184, 18-2, 18-6; and winding section 9 has active conductor portions having the prefix 19-1 and indicated in FIG. 1 as 19-1, 19-2, 19-6.

The active conductor portions 18-1 on winding 8 are connected in series by the end conductor portions having the prefix 16-, and the active conductor portions 19-1 on winding section 9 are connected in series by the end conductor portions having the prefix 17-. The end conductor portions 16-1 through 16-6 and 17-1 through 17-6 are shown in FIG. 1.

In actual practice, one of the windings 6 or 2 is longer than the other by a length equal to the distance over which it is desired to measure or travel.

In accordance with the present invention, the first and second winding sections 8 and 9 are arrayed so that the active conductor portions 18-2 and 19-1, for example, are substantially the same space location relative to the active conductor portions 3- of the first winding 2. Further, winding sections 8 and 9 are connected in series at terminals 11 so that the active conductors 18-2 and 19-1, for example, both conduct in the same direction. Similarly, each of the other pairs of active conductor portions 18-3 and 19-2, 18-4 and 19-3, 18-5 and 19-4, and 18-6 and 19-5 have both conductors in the pair conducting in the same direction. In this manner, each conductor in the pair has substantially the same coupling relationship with the active conductor portions of the first winding 2. The exactness in which the conductors 19-1 and 19-2 are overlayed in the same space is not critical, but the farther apart they are, the lower the combined coupling which results from the pair.

While the active conductor portions of the winding sections 8 and 9 in FIG. 1 are generally connected and Y spatially arrayed to be additive with respect to each other, the end conductor portions 16- and 17- are arrayed to conduct in opposite directions. More specifically, the direction of conduction of th end conductor portion 16-1 is opposite to that of the end conductor portion 17-2. Similarly, the conduction directions for the pairs 17-1 and 16-2, 16-3 and 17-4, and so on are all opposite. The effect of having the active conductor portions arrayed to be additive while the end conductor portions are in alternating opposite directions can be observed with reference to FIG. 2.

In FIG. 1, when an ac signal is energized between terminals 21 and 22, the active conductor portions 18- and 19- give rise as indicated in FIG. 2 to the field vectors l8 and 19 which alternate in direction each half cycle, and cause a voltage at terminals 23 and 24 of FIG. 1. The fields resulting from the end conductor portions also alternate direction in each half cycle so that the net sum-of the end conductor portion fields I6 and 17' in FIG. 2 considered in a clockwise or counterclockwise sense is approximately 0.

The field pattern of FIG. 2, produced by two overlayed winding sections 8 and 9 which comprise the second winding 6 of FIG. 1, is similar to the field pattern generated in accordance with U.S. Pat. No. 2,9l5,72l where that patent uses the different technique of onehalf current return conductors.

The production of the field pattern of FIG. 2 is useful in reducing or neutralizing the effects of constant coupling between the winding of a position-measuring transformer. The reduction in unwanted constant coupling can be explained, for example, in connection with FIG. 3.

In FIG. 3, waveform 25 represents the amplitude of the coupling wave produced beween the active conductor portions 3- of the first winding 2 and the active conductor portions 18- and 19- of the second winding 6. When the second winding 6 and the first winding 2 are moved relative to each other so'that the active conductor portion 3-2 is exactly superposed over the active conductor portion 18-1, the windings are defined for convenience in this specification, to be at the 0 point where maximum coupling occurs. The maximum coupling betwen windings 2 and 6 is indicated by the positive peak in curve 25 in FIG. 3 at the 0 point. When the winding of FIG. 1 are moved relative to each other so that the active conductor portion 3-2 is half-way between active conductors 18-1 and 18-2, the windings are defined to be at the point and have zero coupling as indicated in FIG. 3. When active conductor portion 3-2 is moved to the location over active conductors 18-2 and 19-1, a negative maximum peak occurs as indicated in FIG. 3. Zero coupling again exists at the 270 point, for example, when active conductor 3-2 is half-way between active conductors 18-2 and 18-3. Finally, coupling wave 25 again reaches a positive maximum at the 360 point, for example, when active conductor portion 3-2 is aligned with active conductor portions 18-3 and 19-2.

The transducer of FIG. 1 is useful, for example, in defining null positions of equal spacing. Equally spaced nulls have been used, for example, for defining the spacing of the magnetic tracks in a magnetic disc drive system.

. In FIG. 3, coupling wave 25 is representative of the fundamental coupling wave which results from the coupling between the active conductor portions on the first winding 2 and the second winding 6. In addition to the fundamental coupling wave, however, the end conductor portions 16- and 17- for the second winding 6 also tend to couple to the end conductor portions 17- of the first winding 2. In FIG. 3, the coupling wave for the end conductors 16- is represented by coupling wave 26 (shown dotted). Similarly, the coupling wave for the end conductors 17- is represented by the coupling wave 27 (shown broken). It is apparent from FIG. 3 that coupling wave 26 has an average value represented by line 52 which is off-set or biased with respect to the average value, represented by line 54, of the fundamental coupling wave 25. Similarly, the average value, represented by line 53, of the coupling wave 27 is also biased with respect to the average value of the fundamental Coupling wave 25. I

The coupling of waveform 26 includes an unwanted coupling component which is the constant coupling represented by the displacement between lines 52 and 54. Similarly, the displacement between lines 53 and 54 represents a constant coupling which is the unwanted coupling component of waveform 27.

In accordance with the present invention, the unwanted coupling component of coupling wave 26 is equal to and opposite from the unwanted coupling component of coupling wave 27 so that when algebraically added these unwanted coupling components tend to neutralize each other. More specifically, the sum of coupling waves 26 and 27 is in phase and has zero bias with respect to the fundamental coupling wave 25.

Whenever an unneutralized unwanted coupling component exists, this constant coupling component gives rise to a once-per-cycle or fundamental frequency error. The embodiment of the present invention shown in FIG. 1 neutralizes these unwanted coupling components by having two winding sections arrayed opposite each other in a multi-layer configuration. The constant coupling component of one winding section neutralizes the constant coupling component of the other winding section without interfering with the fundamental coupling of the active conductor portions.

In FIG. 1, two active conductor portions overlay the same space area; for example, active conductor portions 18-2 and 19-1. With two active conductors in the same space position, a two-turn winding is achieved for the active conductors. The end conductors, however, are only one turn since end conductors in FIG. 1 do not occupy the same space location.

Four-Layer Linear Winding Member FIGS. 4 through 7 schematically represent patterns of active conductor arrays as they appear in various stages of a manufacturing process for a two-phase, four-layer transformer member, which is schematically shown in FIG. 7. The transformer member of FIG. 7 includes the constant coupling (or bias) neutralization feature previously described in connection with FIG. 1. The member of FIG. 7 also includes quadrature compensation within each cycle to insure that the polyphase sine (BC) and cosine (AD) windings tend to produce fields displaced in space exactly one-quarter of the space cycle even when the respective winding sections which form the sine and cosine windings are not spaced exactly in quadrature.

Referring to FIG. 4, a schematic representation of an array of active conductors A, specifically Al through A5, is shown. The conductors Al through A are intended to be equally spacedwhere the distance between any adjacent pair of active conductor portions defines one-half the space cycle.

. FIG. 4 alsoincludes an array of active conductors B, specifically, Bl through B5. The active conductors Bl through B5 are spaced substantially identically to the active conductors A1 through A5 and are preferably produced from the same photographic negative. The conductors A and B in FIG. 4 are representative of either a photographic negative or insulated metal conductors on a common base-of metal, glass or plastic, so that the relative position of the active conductors A is fixed with respect to the relative position of the active conductors B. Specifically, active conductors B are shifted a displacement al" from active conductors A where a1 is approximately of the space cycle.

FIG. 5 is also representative of a photographic negative or array of conductors which is substantially identical to the photographic negative or array of conductors represented by FIG. 4. Accordingly, the active conductors C, specifically, Cl through C5, and the active conductors D, specifically DI through D5, are each produced from the respective active conductors Al through A5 and B1 through B5. Accordingly, the displacement, a2, of the active conductors D from the active conductors C in FIG. 5 is substantially identical to the displacement al in FIG. 4.

Referring now to FIG. 6, a representation of a multilayer structure is shown wherein the active conductors represented in or photographically developed from FIG. 5 have been superposed over the active conductors similarly derived from FIG. 4. In FIG. 6, certain of the active conductors in FIGS. 4 and 5 have been removed and end conductor portions for interconnecting active conductor portions have been added. The additions and deletions are by well known printed circuit techniques.

In FIG. 6, four separate winding sections, A, B, C an D are formed where they derive their designations from the active conductor designations of FIGS. 4 and 5 from which they are produced. In FIG. 6, the displacement a1, between winding section A and winding section C is substantially identical to the displacement, a2, between winding sections B and D. The substantial identity of the displacement a1 and a2 derives from the identities in FIGS. 4 and 5 of the displacements a1 and a2. When the layers of FIGS. 4 and 5 are superposed over each other, the B and C active conductor portions are approximately aligned. If, as shown in FIG. 6, a displacement b exists between the D and C winding sections, 011 equals 112, since 111 al" b and a2 a2 b and a1 b a2 b.

The transformer of FIG. 7 is produced by turning the winding sections B and D underneath the winding sections C and A of FIG. 6 so that the two-layers of winding sections of FIG. 6 become four-layers of winding sections in FIG. 7. While during assembly the winding sections B and D may be shifted relative to the winding sections C and A, the C and A and B and D winding sections do not move relative to each other. In FIG. 7, therefore, the angle B between the B and C winding sections may be different from the angle b in FIG. 6 between those same sections. The angles a1 and a2, however, do not vary and are the same as in FIG. 6.

The terminals 32 and 36 from winding sections A and D, respectively, are electrically connected together so that the winding Section A and the winding section D form the complete cosine winding which has input terminals 33 and 37. In a similar manner, terminals 35 and 31 from winding sections B and C are electrically connected together forming a complete sine winding having input terminals 30 and 34. Both the sine winding comprised of the winding sections C and B and the cosine winding comprised of winding sections A and D each individually have the constant coupling neutralization feature previously described in connection with the winding 6 of FIG. 1 for same reasons that winding 6 has that feature as previously described. Also, the sine and cosine windings of FIG. 7-have a quadrature compensation feature which is now further described in connection with FIG. 8.

Quadrature Compensation Referring to FIG. 8, the vectors A(i), B(i), C(i), and D(i) each represent the space location of upper case like-lettered active conductors in FIG. 7. The lower case letter i represents any one of the postscripts from 1 to 5 for the active conductors of FIG. 7. For example, for i 2, the vector diagram of FIG. 8 represents the space locations of the active conductors A2, B2, C2, and D2 of FIG. 7. Similarly, for i" equal to 3, the vector diagram of FIG. 8 represents the space location of the active conductors A3, B3, C3, and D3. As previously indicated in connection with FIG. 7, the vector A2 is displaced an angle al from vector C2, and similarly, the vector B2 is displaced an angle of a2 from vector D2. Furthermore, due to the manufacturing steps discussed in connection with FIGS. 4, 5, 6 and 7, the angle a1 is rendered equal to the angle a2. With this condition of equality, th electrical interconnection of the B and C vectors, for example, B2 and C2, produces a resultant vector BC2 which is generally indicated in FlG.8 as BC(i). Similarly, the interconnection of the vectors A2 and D2, (D2 is the electrical reversal of D2), which are generally indicated as A(i) and D(i) in FIG. 8, produces a resultant vector AD(2) which is generally indicated as AD(i) in FIG. 8.

With the angle between the B and C vectors equal to B, the resultant vector BC is located 3/2 from both the B and C vectors.

The vectors A and D are separated by an angle 5 equal to al [180 a2) 3]. Since a1 is equal to (12, or more generally equal to a, the angle 1; is given as follows: 2 a B I80. The resultant vector AD is therefore, positioned l2 from both the A and D vectors. The angle /2 equals a-fl/Z 90. As can be seen by inspection, the angle between the resultant vectors AD and BC is equal to a/2 [3/2. By substituting the value of /2 as given above into that last expression the angle between the resultant vectors AD and BC is shown to be precisely 90 degrees.

While FIG. 8 has been described by way of example with the postscript value 1' equal to 2, the vector diagram of FIG. 8 applies for all of the postscripts 2 through 4. Since the general space area over which the active conductors couple to the reference winding for each value of the postscript i is less than one space cycle, quadrature compensation is provided individually within each cycle. Having quadrature compensation within each cycle is important in reducing the sensitivity of the quadrature compensation to anomalies. Because the active conductors which contribute to the compensation couple to the same general space area, as distinguished from different, widely separated space areas, the quadrature compensation of the FIG. 7 embodiment is relatively immune to the effects of anomalies.

Referring to FIG. 9, the resultant vector AD(2) is exactly 90 from the resultant vector BC(2) for the reasons explained in FIG. 8. In a similar manner, the vectors A3, B3, C3 and D3 produce resultant vectors AD3 and BC3 which, in accordance with the principles discussed in FIG. 8, are precisely 90 apart. Even though the resultant vectors AD2 and AD3 and the resultant vectors BC2 and BC3 are not precisely aligned, it is apparent that the resultant vectors AD (2,3) BC(2,3) derived therefrom are also exactly 90 apart.

Referring to FIG. 10, the four winding sections A, B, C, and D represent those depicted in FIG. 7. The four winding sections in FIG. 10 are separated and not shown in stacked relation in order to show their details with greater clarity. In FIG. 10, the layers are arranged from the top toward the bottom of the page in the order C, A, B, and D which represents their increasing distance from the scale winding member of the positionmeasuring transformer as shown in FIG. 14.

In FIG. 10, the winding sections A through D are manufactured in the manner previously outlined in connection with FIGS. 4 through 7. Therefore, when the winding sections B and C are interconnected to form the sine winding and the winding sections A and D are interconnected to form the cosine winding, those sine and cosine windings exhibit quadrature compensation. Also, the winding sections B and C and the winding sections A and D each include the constant coupling neutralization feature previously described in connection with FIGS. 1, 2 and 3.

In FIG. 10, winding section C has a plurality of active conductor portions of which active conductor 118 is typical. The active conductor portions are connected together by end conductor portions along margins defined by opposite ends of the active conductor portions where end conductor portions 116 and 117 are typical. The center-to-center spacing of the active conductor portions, for example, between active conductor portions 118 and 119, is equal to the pitch, P, and is the same for all the winding sections A through D in FIG. 10. While the windings have the same pitch and therefore couple with the reference windings of the positionmeasuring transformer with the same fundamental space frequency, the widths, W, of the active conductor portions and the widths, S, of the spaces between active conductor portions vary from winding section to winding section.

Transfonnation Equalization and Harmonic Neutralization The variation in the widths of the active conductor portions relative to the widths of the spaces in FIG. 10 is for two reasons.

First, the ratio of the conductor to space widths is used, in accordance with the general teachings in the US. Pat. No. 2,799,835, to reduce or neutralize the effects of harmonic terms in the coupling signal. Since the third harmonic term is usually the largest contributor to errors, the conductor to space width ratio is usually adjusted to 2-to-l for third harmonic neutralization although other ratios for other harmonics can be selected.

Second, the ratio of the conductor-to-space widths is used to adjust the coupling between the winding sections and the reference winding since the winding sections are located difierent distances from the reference winding to which they couple. The different distances are shown fora typical transducer in FIG. 14 by the dimensions along the left-hand edge. The farther each winding section is from the reference winding, the lower the coupling of that winding section. For the purposes of this invention, the coupling is conveniently described in terms of a transformation ratio which is a ratio of the input signal, I, in the primary winding (e.g., sine or cosine) to the output signal, V, in the secondary winding (e.g., reference winding). In accordance with the present invention, the greater the conductor-tospace width ratio, the lower the coupling and also the lower the resultant transformation ratio. Using this principle, the winding sections which are closer to the reference winding have a greater conductor-to-space width ratio so as to reduce their coupling to the reference winding which therefore reduces their transformation ratio and makes that ratio more nearly equal to the transformation ratio of the farther away winding sections.

In FIG. 10, the width of the active conductor portions for the winding sections A, B, C and D are given by WA, WB, WC, and WD, respectively. In a similar manner, the widths of the spaces between active conductor portions for the winding sections A, B, C and D are given by SA, SB, SC, and SD, respectively. The widths of the conductor portions WC and WA for the winding sections C and A are equal as are the widths WB and WD of the conductor portions for the winding sections B and D. The winding sections C and A are closer to the reference winding than the winding sections B and D as shown in FIG. 14.

Referring to FIGS. l2, l3 and 14, the manner in which the winding sections A through D of FIG. 10, are positioned over each other to form a multi-layer, polyphase member 134 is shown. In FIG. 13, the layers of conductors for winding sections C, A, B, and D are shown progressively removed from a base layer 136.

In FIG. 14, the polyphase member 134 is shown heneath a scale member 128. A typical construction for the polyphase member 134 includes the B and D winding section layers clad to opposite sides of a plastic insulating layer 138 and the winding section layers C and A clad to the opposite sides of an insulating plastic layer 140. The B, 138, D laminate is adhered to the base 136 by another insulating and adhesive layer 137. In a similar manner, the C, 140, A laminate is adhered to the surface of the B layer by an adhesive and insulating layer 139 between the A and B layers. An electrostatic shield 142, of the type described in US. Pat. No. 3,090,934, is adhered to the C layer by an insulating and adhesive layer 141.

Positioned above the polyphase member 134 is the scale or reference winding member 128 constructed in a manner well known in the art. Member 128 typically includes a continuous reference winding layer 131 adhered by layer 130 to a base 129. The layer 131 includes a winding of the type previously depicted schematically as winding 2 in' FIG. 1. The thickness dimensions for a typical multi-layer structure are shown in fractions of an inch along the left-hand side of FIG. 14. While these dimensions are not critical, selection of different thicknesses results in different transformation ratios which require different conductor-to-space width ratios for compensation.

As previously discussed in connection with FIG. 10, the conductor-to-space width ratio of the. various winding sections is varied in order to compensate for the differences in coupling between the winding sections and the reference windings as conveniently measured as differences in transformation ratio, which are principally due to the differences in displacement of the In FIG. 12, pairs of typical active conductor portions for each of the winding sections C, A, B, and D are shown below a reference winding represented by three typical active conductors R1, R2, and R3. In FIG. 14, the conductors R1, R2 and R3 are contained in the reference winding layer 130. Again referring to FIG. 12, the center-to-center spacing of all the active conductors equals the pitch, P where thespace cycle is equal to 2?. The width of each active conductor portion for the reference member is equal to WR' and the spaces between adjacent active conductors is equal to SR. In accordancewith the teachings of the US Pat. No.

. 2,799,835, the conductor-to-space ratio therein is 2-tol for cancellation of unwanted thirdharmonics. This 2-to-l ratio is achieved by having WR equal 2SR. Briefly, the third harmonic cancellation results because the width of the WR equals one-third of 2?. Accordingly, WR is exactly equal to one period of the third harmonic space cycle. The average of a sinusoid over exactly one period is zero so that the average coupling of each conductor bar R1, R2 and R3 tends to be zero with respect to third harmonics. For a further discussion of the principles of harmonic cancellation reference is made to the above-referenced US. Pat. No. 2,799,835.

It is also possible to make the conductor-to-space ratio for each of the winding sections A, B, C, and D equal to 2-to-1 for neutralizing unwanted third harmonic coupling. Alternatively, however, the conductor-to-space width ratios is varied from 2-to-1 in order more nearly to equalize the transformation ratios of each of the layers.

In order to equalize the coupling to the reference winding and therefore the transformation ratio between the winding section B to that of the winding section C to which it is connected, the widths of the conductors for winding section C are made greater than those for winding section B. In a similar manner, the

widths of the conductors for the winding section A are made greater than the widths for the winding section D. If full equalizationof all the winding sections is desired, the widths of the active conductors for winding section C are made greater than for those of A which in turn are made greater than for those of B which in turn are made greater than for those of D.

For simplicity in manufacture, however, full equalization is not employed in the winding sections of FIG. 10. Rather, winding sections C and A have the same conductor-to-space width ratio and similarly, winding sections B and D have equal conductor-to-space width ratios different from the ratio for C and A. More specifically, for the general thicknesses and displacements previously indicated in connection with FIG. 14, it has been found that a width of 0.0393 for the conductors and 0.0107 inch for the space for the winding sections C and A produces good results when the conductor widths are 0.0273 and the spaces are 0.0227 inch for the winding sections B and D.

For the above-discussed dimensions of FIGS. 10 and 14 the coupling from winding section C is of the order of 1.45 times the coupling of winding section B to the reference winding. In a similar manner, the coupling of the winding section A is of the order of 1.45 times the coupling of winding section D. In order to render the coupling of winding section C equal to the coupling of winding section B and the coupling of winding section A equal to the coupling of the winding section D, the

transformation ratios of the winding sections C and A, are both reduced by increasing their conductor-tospace width ratios while the transformation ratios of the winding sections B and D are both increased by decreasing their conductor-to-space width ratios.

The required change in conductor-to-space width ratio can be determined both experimentally and mathematically. For an approximation of the mathematics employed to calculate the desired change in conductorto-space width ratio, a winding having a 2-to-1 conductor to space width ratio is initially considered. A decrease in transformation ratio is achieved by widening that conductor an amount A by symmetrically adding M2 on either side of the center line, thereby increasing the conductor-to-space width ratio. Addition of an incrementalvalue on either side of that conductor is an addition at points separated approximately 120 with respect to the fundamental space cycle. The sum of two vectors spaced at 120 is lower than the sum of all the incremental vectors spaced at angles less than 120". The actual summation across the full width of a conductor can be made employing integral calculus. By way of approximation, it is assumed that in the region in question, the change in transformation for the fundamental signal is approximately linear. The change, A, in width required therefore to equalize the transformation ratios TB and TC representing the coupling of winding sections B and C, respectively, to the reference winding is derived as follows:

Eq. (1) Given:

[TB/TC], I/l.45 WC WB 0.0333

Therefore:

KB/KC =1/(1.45)

In order to equalize transformation ratios, that is, to make TB TC, the widths WC and WB are changed an amount, A, whereby Eq. (1) becomes:

[0.0333 A/0.0333 A] [l/l.45 TB/TC=1 Eq. (2) Solving Eq. (2) for A yields,

A 0.006 inch Where:

TC transformation ratio, Vout/Iin, representing the coupling of winding section C to the reference winding TB transformation ratio, Vout/fin, representing the coupling of winding section B to the reference winding WC width (0.0333 inch) of conductor for winding section C having a space cycle 0.1 inch [TB/TC],, measured value of ratio of TC/TB before change of A WB width (0.0333 inch) of conductor for winding section B having a space cycle 0.1 inch KC constant of proportionality for winding section.

duce WC and WA equal to 0.0393 inch, thereby reducing the space widths SC and SA to 0.0107 inch. In a similar manner, 0.006 inch is subtracted from the nominal value 0.0333 to produce the width WB and WD equal to 0.0273 inch thereby increasing the space widths SB and SD to 0.0227 inch. Note that the average width of WC and WB is 0.0333 and of WA and WD is also 0.0333 so that on an average the sine winding (BC) and the cosine winding (AD) active conductors have a 2-to-1 conductor-to-space width ratio.

The above calculations for A were determined with principal consideration to the coupling of the winding sections at the fundamental space frequency. The effect of the coupling at the third harmonic of the fundamental space frequency for delta equal to 0.006 inch is different than for the fundamental space frequency. After modification by 0.006, the conductor-to-space widthratio in FIG. 10 is not precisely 2-to-l and therefore each conductor portion does not individually cancel the effects of third harmoniccoupling-Notwithstanding this lack of complete third harmonic cancellation, the average conductor-to-space width ratio for the series connected winding sections C and B and similarly the winding sections A and D, is 2-to-I as indicated above. For this reason, any increase in third harmonic coupling due to the increase in conductor-tospace width ratios of the C and A winding sections tends to be negated by an opposite change in the third harmonic coupling of the B and D winding sections, respectively.

Because the conductor-to-space width ratios were not selected at four different values, in order to equalize the transformation ratios for all four winding sections in FIG. 10, the sine winding sections A and C generally have a resultant transformation ratio which is greater than the transformation ratios of the cosine winding sections B and D. Because the quadrature compensation feature of the present invention generally requires equal transformation ratios, a further adjustment of the transformation ratios of the FIG. 10 winding sections is required. That adjustment is made, referring to FIG. 7, by placing a conventional resistor, not shown, between the terminals 34 and 30 of the SIN winding. In this manner, the current in the SIN winding is reduced relative to that of the COS winding to compensate for the greater transformation ratios of the SIN winding sections. The SIN winding has a greater transformation ratio because as is apparent from FIG. 12 and 14, the sine winding sections C and B are closer on an average to the reference winding than the cosine winding sections A and D. The feature of using a resistor across one of the windings of a position-measuring transformer is called line balancing.

The present invention insures that, through quadrature compensation, the sine and cosine windings tend to be exactly apart. In accordance with another feature of the present invention, the quadrature can be adjusted also by placing a resistor across one or more of the winding sections. For example, a resistor connected between terminal 32 and terminal 33 reduces the coupling of the winding section A to the reference winding. Referring now to FIG. 8, a resistor between terminals 32 and 33 causes a reduction in the length of the vector A(i) which tends to rotate the resultant vector AD(i) clockwise. If the angle between the resultant vectors AD(i) and BC(i) is greater than 90, indicating a lack of exact quadrature, the resistor between terminals 32 and 33 in FIG. 7 tends to correct-the quadrature error. Similarly, for angles less than 90, a resistor between terminals 37 and 36 causes a counter-clockwise rotation of vector AD(i) which tends to correct the quadrature error.

A resistor placed between the terminals 30 and 34 or between the terminals 33 and 37 in FIG. 7 shortens the resultant vectors AD(i) and BC(i), respectively, in FIG. 8 without affecting the angle between them. A resistor between the terminals of any winding section, that is, from terminals 32 and either 33 or 37 or between terminals 35 and either 30 or 34, results in a change in the angle between the resultant vectors. Means are provided, therefore, for adjusting the line balance, that is the relative coupling of the sine and cosine windings, and also means are provided for adjusting the quadrature between sine and cosine windings.

Referring to FIG. 11, the horizontal lead conductors 91, 92, 93 and 94 correspond to the horizontal likenumbered lead conductors in FIG. 10. Note that the sine winding lead conductors 91 and 92 are superposed and electrically connected to conduct in opposite di rections in order to neutralize any unwanted coupling of those lead conductors. As shown in FIG. 11, the terminals 32 and 36 are jumpered together to interconnect the two cosine winding sections indicated as A and D in FIG. 10..Similarly, the terminals 31 and 35' are jumpered together to interconnect the two sine winding sections indicated as B and C in FIG. 10. The terminals in FIG. 11 are numbered, with primes added, the same as the corresponding terminals in FIG. 7.

Also indicated in FIG. 11 are the adjusting resistors 96 and 97. Resistor 96 connected between cosine terminals 32 and 33 has the effect of adjusting the angle between the sine and cosine windings, that is, adjusting the quadrature. Resistor 97 connected'between cosine terminals 33 and 37 is operative to adjust the current in the cosine winding relative to the sine winding and accordingly is the line balancing resistor. While resistors 96 and 97 have been shown connected between cosine terminals, resistors may be placed between any of the terminals in FIG. 11 in order to adjust the relative coupling of any winding section or any combination of winding sections as is desired.

While the embodiment discussed in connection with FIGS. 7 through 14 has windings each of which includes two winding sections which, for manufacturing convenience, are constructed by turning one winding section over with respect to the other, the turned over relationship can be achieved without any actual mechanical turn over if desired. For example, the end conductor portions may be added by well-known photographic techniques along either margin without any mechanical turn over of the active conductor portions.

MultLCycle Rotary Transducer In FIGS. 15 through 21, a multi-cycle, rotary transducer is shown. That transducer employs the constant coupling neutralization feature previously described in connection with FIGS. 1 and 7, the quadrature compensation feature previously described in connection with FIGS. 4 through 9, the harmonic cancellation feature and the transformation ratio adjustment feature previously described in connection with FIGS. through 14.

The pattern of FIG. schematically represents an array of conductors or alternatively a photographic negative for producing an array'of conductors. Specifically, the pattern of FIG. 15 includes an array A of radial conductors A10 through A which is fixed in space relative to a second array B of radial conductors B10 through B80. The pattern of FIG. 15 for rotary devices is analogous to the previously described pattern of FIG. 4 for linear devices. The radial spacing of the conductors in array A is substantially identical to the radial spacing of the conductors in array B. The A and B arrays are preferably made from the same photographic negative so as to be identical. The array B, however, is rotated mechanical degrees plus onequarter of the space cycle of the array A. The space cycle is equal to twice the angular displacement of two adjacent conductors. The rotation of array B with respect to array A can be observed by noting the location of the A10 and B10 conductors.

Referring to FIG. 16, a second pattern identical to the pattern of FIG. 15 is depicted which includes an array C of radial conductors C10 through C80 and an array D of radial conductors D10 through D80. The pattern of FIG. 16 is preferably an exact copy of the pattern of FIG. 15 made, for example, using photographic techniques. Note that the pattern of FIG. 16 is rotated l80 in space, about an axis perpendicular to the plane of the paper, with respect to the pattern of FIG. 15. The array D is preferably a photographic print ofthe array A and similarly the array C is preferably a print of the array B so that the conductor D10 corresponds to the conductor A10 and the conductor C10 corresponds to the conductor B10.

Referring to FIG. 17, a double layer array is formed by placing the FIG. 16 pattern over the FIG. 15 pattern so that array C is over and concentric with array A and array D is over and concentric with array B. FIG. 17 for rotary devices is analogous to the previously described FIG. 6 for linear devices. In the pattern of FIG. 17, the angle between the B and D conductors is identical to the angle between the A and C conductors. This identity is created by the assembly steps carried out as described in connection with FIGS. 15, 16 and 17.

Referring to FIG. 18, only the conductors with postcripts 10 in FIG. 17 are schematically shown. The angle, a, between the B10 and D10 condyctors is rqual to the angle, a, between the A10 and C10 conductors. When the pattern of arrays D and B are folded under and stacked concentric with the pattern of arrays C and A, as further described hereinafter in connection with FIG. 20, any misalignment of the A and D conductors is indicated as an angle b" in FIG. 18.

Referring to FIGS. 18, 20 and 21, further details of the multi-cycle rotary transducer member are shown. As indicated, the FIG. 20 four-layer pattern is formed using the conductors from the pattern of FIG. 17 by folding the arrays D and B under the arrays C and A about line 41. Additionally, the pattern of FIG. 20 has end conductor portions of which end conductor portions 62, 63, 64 and 65 are typical, added to interconnect adjacent radial conductor patterns in a manner analogous to the end conductors added in FIG. 6. For ease in observing the four separate layers of winding sections, FIG. 19 depicts each separate winding section in the array order of C, A, B and D in which the winding sections are stacked from top to bottom. Note that the C, A, B, and D order for the rotary device is the same as for the linear device as previously shown and described in connection with FIGS. 10, and 14. Since FIGS. 19 and 20 are schematic, the various insulating and adhesive layers which separate the winding sections have not been shown but are, of course, present in the same manner as described previously in connection with FIG. 14.

Referring to FIG. 21, a vector diagram is depicted which illustrates the quadrature compensation feature in the rotary device of FIG. 20 in a manner analogous to the illustration in FIG. 8 of the quadrature compensation feature for the linear device of FIG. 7. As is illustrated in FIG. 21, the resultant vactor A'D', representing the resultant space position of the cosine winding formed by the cosine winding sections A and D, tends to be precisely 90 displaced from the resultant vector CB' representing the space position of the sine winding formed by the sine winding sections C and B. Briefly the angle, d), between vectors C and B equals (180 a2 +3) al. Since (11 =a2 =01, =2a+ [3 I80 and /2 a [3/2 90. The angle between resultant vectors AD and CB', as can be observed in FIG. 21, is a B/2 l2 which, by substituting the value for l2 of the previous sentence, is shown to be precisely 90.

The constant coupling neutralization feature is incorporated in the FIG. 20 embodiment since, also referring to FIG. 19, the sine winding sections C and B are connected by jumper 47 to have their end conductor positions conduct in opposite directions. Similarly, the cosine winding sections A and D are connected by jumper 46 so that their end conductor portions conduct in opposite directions.

More specifically, still referring to FIGS. 19 and 20, a plurality of end conductor portions (e.g., 62) at each end of each winding section is proximate to one of the intervening spaces between the adjacent end conductor portions (64,68) of the other winding section in the same margin.

In order to incorporate the harmonic cancellation and transformation ratio adjustment features into the rotary device of FIG. 20, the conductor-to-space width ratio is changed in a manner analogous to that previously described. In FIG. 20, for an ideal transducer the conductor portions and the spaces between them are wedge-shaped. Because of this shape, both the conductor portions and the spaces between them increase in width as a function of the distance from the center of the pattern. For simplicity in design, however, the space between conductor portions are made rectangular in shape while the conductor portions are wedge shaped as shown, for example, in the above referenced US. Pat. No. 2,799,835. The width of the rectangular space is made equal to the average width of a wedgeshaped space. The average width for a wedge-shaped space is the width at that point which is half way between the innermost point along a radial conductor and the outermost point. The conductor-to-space width ratio is, for convenience, determined at the location which is half way between the inner and outer ends of the radial conductors. In this manner, the conductorto-space width ratios for each of the winding sections of FIG. l9 are readily adjusted in the same manner as previously described in connection with FIGS. through 14.

The transducer of FIG. 20 includes only four space cycles per revolution. In actual practice, however, transducers having many more active conductors are employed to produce a greater number of cycles per revolution, for example, 360 space cycles or more per revolution.

Two-Layer Linear Transducer Referring to FIG. 22, a two-layer, polyphase windings 154 is schematically shown in coupling relation to a reference winding 155. The actual dimensions are typically like those in FIG. 10. The polyphase windings 154 include a SIN winding and a COS winding formed of winding sections B and C and winding sections A and D, respectively. The winding sections B and C are on the same upper layer and the winding sections D and A are on the same lower layer where those two layers are, for example, on opposite sides of an insulator (not shown).

The polyphase windings 154 are preferably produced in the manner outlined in connection with FIGS. 4, 5 and 6. More specifically: the pattern consisting of array C over array A like that in FIG. 6 is produced to the right in FIG. 22 while the pattern consisting of array D over array B like that in FIG. 6 is turned over to form B over D and produced to the left in FIG. 22. For example, the device of FIG. 22 can be produced by cutting the FIG. 6 pattern along an imaginary line between the C over A and the D over B patterns and thereafter turning over the latter to form the B over D pattern. Thereplacement, al, between the A and C winding sections 7 is identical to the displacement, (12, between the B and D winding sections for the reasons discussed in connection with FIG. 6. Therefore, thequadrature compensation feature previously discussed 'in connection with FIG. 7 also applies to the FIG. 22 embodiment of the invention.

In addition to quadrature compensation, the SIN and COS windings in FIG. 22 each separately include two continuous winding sections arrayed to neutralize constant coupling. For example, the SIN winding is comprised of the B and C winding sections where the end conductor portions of sine section B, of which end conductor portions 56, 57 are typical, are arrayed in opposite margins to conduct in the opposite direction of the end conductor portions of sine section C, of which end conductor portions 58 and 59 also in opposite margins are typical. As is apparent by inspecting FIG. 22, the coupling of reference winding to the end conductor portions 56 and 57, for example, is like that represented by curve 26 in FIG. 3. Similarly the coupling of reference winding 155 to the end conductor portions 58 and 59, for example, in FIG. 22 is like that represented by curve 27 in FIG. 3. As described in connection with FIG. 3, the constant coupling of one set of end conductors (56 and 57) is equal and opposite to the constant coupling of the other set (58 and 59). The COS winding in FIG. 22 similarly has the constant coupling neutralization feature.

In addition to the aforementioned features, the polyphase windings 154 of FIG. 22 also employ the constant coupling, the harmonic neutralization and cou- 

1. A position-measuring transformer having relatively movable winding members, one of said members including a continuous reference winding, another of said members consisting of a first pair of polyphase winding sections positioned approximately in space quadrature with respect to each other and a second pair of polyphase winding sections positioned approximately in space quadrature with respect to each other, one winding section of both pairs being in circuit with each other and the other winding sections of both pairs being in ciRcuit with each other, said first and second pairs of winding sections being overlaid with respect to each other in separate layers and having means compensating for departure from space quadrature relation with each other, each of the winding sections of each of said pairs consisting of a continuous array of uniformly spaced parallel conductor bars.
 2. The transducer of claim 1 wherein, the first winding section for one polyphase winding is arrayed relative to one of the winding sections of another polyphase winding with a displacement Alpha , and the second winding section for said one polyphase winding is arrayed relative to the other winding section of said another polyphase winding with the same displacement Alpha , where Alpha is the same in the above cases and represents 90* plus an error which is the same in both cases.
 3. The transducer of claim 2 wherein each of the winding sections for said one polyphase winding is arrayed opposite respective winding sections for said another polyphase winding forming a multi-layer configuration.
 4. The transducer of claim 3 wherein all of said winding sections are arrayed opposite each other forming a four-layer configuration, at least one conductor bar in each one of all of said winding sections being located in the same space cycle defined as twice the dimension center-to-center of adjacent conductor bars, the dimension of the space cycle being substantially the same for all of said winding sections.
 5. The transducer of claim 4 wherein said first winding sections of said polyphase windings are arrayed closest to said first winding and wherein the conductor-to-space width ratio of said first winding sections is greater than the active conductor-to-space width ratio of said second winding sections.
 6. The transducer of claim 5 wherein the average of the conductor-to-space width ratios for said first and second winding sections for each of said polyphase windings, is approximately 2-to-1 whereby the third harmonic coupling between said polyphase windings and said first winding tends to be neutralized.
 7. A position-measuring transducer including N windings, W(1), . . . , W(N) arrayed on one member to couple with a reference winding on another member with N coupling signals each having a different space phase equal to a different integral multiple of 360/N degrees, the improvement wherein, each of said windings of said one member consists only of N winding sections there being a total of N2 winding sections where each of said winding sections, WS(i,j), is identified by different values of ''''i'''' and ''''j'''' from l to N, said winding sections, WS(i, j), arrayed in N patterns, said patterns shifted relative to each other approximately 360/N degrees, each pattern identified by a different value of i 1, . . . , N where each pattern includes N substantially identically arranged winding sections each identified by a different value of j 1, . . . , N; said winding sections, WS(i, j), connected as follows to form said windings W(1), . . . , W(N) with space phases which tend to be exactly 360/N degrees apart: W1 WS (1, 1), WS(2, 2), . . . , WS(N, N) W2 WS(1, 2), WS(2, 3), WS(3, 4), . . . , WS(N-1, N) WS(N, 1) '''' '''' '''' WN WS(1, N), WS(2,1), WS(3, 2), . . . , WS(N, N-1).
 8. The transducer of claim 10 wherein N equals 3, thereby forming a three-phase system wherein the windings W(1), W(2), and W(3) tend to be exactly 120* apart and wherein three substantially identical winding section patterns WS(1,1), WS(1, 2), WS(1,3); WS(2,1), WS(2,2), WS(2,3); and WS(3,1), WS(3,2), WS(3,3) are interconnected as follows: W(1) WS(1,1), WS(2,2), WS(3,3) W(2) WS(1,2), WS(2,3), WS(3,1) W(S) WS(1,3), WS(2,1), WS(3,2).
 9. The winding of claim 1 wherein adjacent ones of active conductor portions for each winding section are inter-connected by end conductor portions to cause adjacent active conductor portions to conduct in opposite directions, first and second winding section means arrayed and electrically connected such that the end conductor portions on one winding section means conduct in the opposite direction of the end conductor portions of the other winding section means.
 10. The winding of claim 9 wherein the number of end conductor portions interconnecting the ends of the active conductor portions in one direction for one of said winding section means is substantially equal to the number of end conductor portions interconnecting the active conductor portions along the end in the same direction of the other winding section means.
 11. A position-measuring transformer having relatively movable winding members, one of said members including a reference winding having at least one phase, another of said member having windings in four layers, including a first pair of winding sections positioned approximately in space quadrature with respect to each other, and a second pair of winding sections positioned approximately in space quadrature with respect to each other, one of the winding sections of said first pair having a space position in phase with the space position of one of the winding sections of said second pair and electrically connected in aiding relation; the other winding sections of said first pair having a space position 180* shifted in phase with respect to the space position of the other winding section of said second pair and electrically connected in opposite directions whereby the error of quadrature of the first and second pair of windings are mutually subtracted.
 12. The transducer of claim 1 wherein, the first winding section for one polyphase winding is arrayed relative to one of the winding sections of another polyphase winding with an undesired space phase error, the second winding section for said one polyphase winding is arrayed relative to the other winding section of said another polyphase winding with substantially the same said undesired space error in the opposite direction.
 13. The transducer of claim 1 wherein said winding sections are in the form of a spiral array.
 14. A position-measuring transformer comprising, a reference winding, first and second polyphase windings coupling to said reference winding with space phases in quadrature of a fundamental space cycle, said polyphase windings have means providing quadrature compensation within the space cycle and wherein said polyphase windings are in multiple layers and wherein the winding sections in one layer have a different conductor width-to-space ratio than the winding sections in another layer.
 15. The transformer of claim 14 wherein one or more winding sections of said polyphase windings is connected in parallel with a resistor comprising said means providing said quadrature compensation.
 16. The transducer of claim 4, one conductor bar in each one of all of said winding sections being located in the same half cycle space.
 17. The transducer of claim 4 wherein successive space cycles of said polyphase windings each contain a conductor bar from each of said winding sections.
 18. The transducer of claim 11 comprising means for obtaining equality of gain between said first and second winding sections.
 19. The transducer of claim 18 wherein said means comprises a resistor in shunt to one of said sections.
 20. The transducer of claim 18 wherein said windings in four layers have a different amount of conductor width-to-space ratios in different layers.
 21. Transformer according to claim 11 including a resistor in shunt to one of said sections to adjust the space angle between (a) one of the winding sections of the first pair and of the second pair and (b) the other winding sections of said first and second pairs, and another resistor in shunt to all of the windings of (a) or (b) to obtain line balance.
 22. A position-measuring transformer having relatively movable winding members, one of said members including a continuous reference winding of discrete space cycles, another of said members consisting of a plurality of windings overlaying each other comprising at least four co-functionally related conductors positioned within a discrete space cycle of the reference winding and means connecting said windings in co-functional compensating relation.
 23. A position-measuring transformer having relatively movable winding members, one of said members consisting of one plurality of polyphase winding sections positioned approximately in co-functional relation to each other, and at least another plurality of polyphase winding sections positioned in the same co-functional relation to each other, a winding section of each plurality being in circuit with a winding section of other pluralities, all of said winding sections being overlaid with respect to each other in separate layers and means whereby said windings are self-compensating for departure from the co-functional relation with each other, each of the winding sections of each of said pluralities consisting of a continuous array of uniformly spaced parallel conductor groups. 